The River Ouse Project: Meadows Surveys Analysis

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1. Introduction

Without going into details, I have built a model that identifies “latent communities” (LC) in the meadows data. There is no intention to classify sites in the NVC sense. Instead, the idea is that the latent communities may be more or less expressed at any site. So what follows is a description of the latent communities, and an analysis of their expression by survey site.

At a quick look, it appears to me that the LC expressions make at least some sense in terms of what we already know about the sites. If that impression holds up to further scrutiny, then I think that the model will help us to relate the patterns that we see to physical, ecological and historical aspects of the environment. I have tried to encapsulate this idea in Figure 1. Here we have the latent communities on the left and their manifestation at the survey sites on the right. In between, the boxes labelled “Environment” are what is called in the literature a “filtering framework”. I quote: “the abiotic conditions define the environmental filters selecting species from a regional species pool …” (Munkemiller et al 2020). My scheme agrees with this in the presence of a filtering framework, but the latent communities are NOT the same as a species pool, also known as a Community Pool (CP). Here’s the difference:

• Community Pool envisages a set of species that may be drawn upon to make up the community manifest at a particular site.
• Latent Community envisages a set of communities that may be drawn upon to make up the mix of species manifest at a particular site.

The conceptual distinction is significant:

• several latent communities may be manifest at a site.
• latent community expression can calculated conveniently.
• in estimating LC expression, dissociative relationships can be taken into account.
• partial LC membership is included in a natural way.

Figure 1.

2. Latent communities

According to this scheme, a latent community is a set of relationships between pairs of plants such that they occur together in the data more or less frequently than would be expected by chance (p < 0.05). These plant pairs are called dyads, and they may be associative (occur together more frequently than would be expected) or dissociative.

Dyads, not plants, are counted in assessing latent community expression at a site; in order count towards LC expression, both elements of the dyad must be present, and the contribution that they make is determined by the sign (associative/dissociative) of the link between them, see Calculation of LC expression below.

Table 1. Model parameters

LC1	LC2	LC3	LC4	LC5	LC6	LC7	LC8
0.858	0.517	0.223	0.481	0.071	0.022	0.188	0.003
0.517	0.596	0.169	0.110	0.226	0.055	0.080	0.009
0.223	0.169	0.635	0.024	0.049	0.254	0.120	0.014
0.481	0.110	0.024	0.565	0.071	0.085	0.072	0.008
0.071	0.226	0.049	0.071	0.260	0.079	0.011	0.017
0.022	0.055	0.254	0.085	0.079	0.206	0.011	0.030
0.188	0.080	0.120	0.072	0.011	0.011	0.076	0.015
0.003	0.009	0.014	0.008	0.017	0.030	0.015	0.035

The dyads are the observed data. The statistical model (Stochastic Block Model) builds a representation of the uncertain nature of the data by assigning probabilities to the links. The probabilities form blocks such that the probability of links between dyads within a block differs from the probability of links between dyads ending in different blocks. Generally, in-block probabilities are greater than out_block probabilities, forming positive groups of dyads. In our case, there are eight blocks. The model is summed up by an 8x8 matrix. The values on the leading diagonal are the in-block probabilities, the off-diagonal values are the probabilities of finding links between the corresponding blocks. The matrix is shown in Table 1. The in_block probabilities in the leading diagonal are shown in bold face, and the text is red when the in_block probability is greater than the out_block probabilities. Latent communities (blocks) 1 - 5 are good, 6 needs to be treated with caution, and the probabilities for 7 and 8 are so low that they may best be ignored (the probabilities are about 1/3 that of LC6, and they contain species that are poorly represented in the data).

I don’t want to go into details of the Stochastic Block Model here, but it is worth mentioning that it is not told anything about the associative or dissociative nature of the links it is modelling. That information is added later.

Details of the Latent Communities follow. For each, there is a graph and a table. The graphs are useful in visualising the contribution of associative and dissociative links. The size of the species symbols is an indication of the species frequency in the data. The tables list the species in the dyads of which the LC is composed.

Latent Community 1.

Latent Community 1 species

name	count	frequency
Anemone_nemorosa	11	6.96
Carex_caryophyllea	12	7.59
Carex_flacca	35	22.2
Lathyrus_montanus	9	5.70
Leontodon_hispidus	13	8.23
Lolium_perenne	111	70.3
Pimpinella_saxifraga	17	10.8
Potentilla_erecta	27	17.1
Potentilla_sterilis	9	5.70
Pseudoscleropodium_purum	23	14.6
Rhinanthus_minor	11	6.96
Rhytidiadelphus_squarrosus	36	22.8
Stachys_betonica	12	7.59
Succisa_pratensis	19	12.0

Latent Community 2.

Latent Community 2 species

name	count	frequency
Achillea_millefolium	71	44.9
Ajuga_reptans	42	26.6
Alopecurus_pratensis	78	49.4
Calliergon_cuspidatum	50	31.6
Centaurea_nigra	71	44.9
Conopodium_majus	21	13.3
Dactylorhiza_fuchsii	28	17.7
Genista_tinctoria	9	5.70
Hypochaeris_radicata	50	31.6
Leucanthemum_vulgare	35	22.2
Lotus_corniculatus	129	81.6
Lotus_uliginosus	102	64.6
Luzula_campestris	79	50
Plantago_lanceolata	59	37.3
Prunella_vulgaris	88	55.7
Ranunculus_bulbosus	30	19.0
Veronica_chamaedrys	58	36.7

Latent Community 3.

Latent Community 3 species

name	count	frequency
Achillea_ptarmica	7	4.43
Angelica_sylvestris	13	8.23
Carex_panicea	6	3.80
Cirsium_palustre	46	29.1
Equisetum_arvense	13	8.23
Galium_palustre	16	10.1
Hypericum_tetrapterum	11	6.96
Juncus_acutiflorus	26	16.5
Juncus_articulatus	11	6.96
Juncus_conglomeratus	29	18.4
Juncus_effusus	43	27.2
Lychnis_flos-cuculi	7	4.43
Mentha_aquatica	6	3.80
Oenanthe_crocata	8	5.06
Pulicaria_dysenterica	20	12.7
Ranunculus_flammula	8	5.06

Latent Community 4.

Latent Community 4 species

name	count	frequency
Agrostis_canina_spp_montana	15	9.49
Briza_media	6	3.80
Cerastium_fontanum	134	84.8
Cirsium_arvense	94	59.5
Danthonia_decumbens	6	3.80
Equisetum_telmateia	3	1.90
Hieracium_pilosella	7	4.43
Hyacinthoides_non-scripta	12	7.59
Poa_trivialis	122	77.2
Ranunculus_acris	140	88.6
Ranunculus_repens	145	91.8
Trifolium_repens	140	88.6
Veronica_officinalis	6	3.80
Viola_riviniana	8	5.06

Latent Community 5.

Latent Community 5 species

name	count	frequency
Anthoxanthum_odoratum	144	91.1
Arrhenatherum_elatius	25	15.8
Bellis_perennis	8	5.06
Brachythecium_rutabulum	117	74.1
Bromus_hordeaceus	27	17.1
Carex_hirta	48	30.4
Cerastium_glomeratum	8	5.06
Cynosurus_cristatus	54	34.2
Dactylis_glomerata	105	66.5
Eurhynchium_praelongum	56	35.4
Festuca_rubra	106	67.1
Geranium_dissectum	31	19.6
Heracleum_sphondylium	26	16.5
Lathyrus_pratensis	78	49.4
Phleum_pratense	85	53.8
Plantago_major	8	5.06
Potentilla_reptans	59	37.3
Rumex_acetosa	130	82.3
Stellaria_graminea	120	75.9
Taraxacum_officinale	109	69.0
Tragopogon_pratensis	6	3.80
Trifolium_dubium	34	21.5
Trifolium_pratense	92	58.2
Veronica_serpyllifolia	57	36.1
Vicia_cracca	17	10.8
Vicia_sativa	17	10.8
Vicia_tetrasperma	19	12.0

Latent Community 6.

Latent Community 6 species

name	count	frequency
Agrimonia_eupatoria	16	10.1
Calystegia_sepium	4	2.53
Cardamine_flexuosa	3	1.90
Cardamine_pratensis	58	36.7
Carex_ovalis	21	13.3
Cruciata_laevipes	7	4.43
Dactylorhiza_praetermissa	3	1.90
Deschampsia_cespitosa	12	7.59
Festuca_arundinacea	11	6.96
Festuca_pratensis	24	15.2
Filipendula_ulmaria	12	7.59
Galium_aparine	17	10.8
Glechoma_hederacea	15	9.49
Glyceria_fluitans	7	4.43
Juncus_inflexus	9	5.70
Lapsana_communis	3	1.90
Myosotis_discolor	8	5.06
Poa_annua	7	4.43
Ranunculus_ficaria	11	6.96
Rubus_fruticosus	16	10.1
Rumex_crispus	15	9.49
Rumex_obtusifolius	36	22.8
Senecio_jacobaea	28	17.7
Stachys_sylvatica	3	1.90
Urtica_dioica	13	8.23
Veronica_beccabunga	4	2.53

Latent Community 7.

Latent Community 7 species

name	count	frequency
Agrostis_canina	22	13.9
Carex_pilulifera	3	1.90
Holcus_mollis	7	4.43
Hypericum_perforatum	4	2.53
Hypericum_pulchrum	5	3.16
Lathyrus_nissolia	4	2.53
Luzula_multiflora	8	5.06
Mentha_arvensis	5	3.16
Pedicularis_sylvatica	3	1.90
Primula_veris	5	3.16
Pteridium_aquilinum	5	3.16
Rumex_acetosella	3	1.90
Silaum_silaus	9	5.70
Stellaria_alsine	5	3.16

Latent Community 8.

Latent Community 8 species

name	count	frequency
Alopecurus_geniculatus	11	6.96
Atrichum_undulatum	4	2.53
Carex_laevigata	2	1.27
Carex_otrubae	2	1.27
Cirsium_vulgare	5	3.16
Convolvulus_arvensis	6	3.80
Crepis_capillaris	4	2.53
Dactylorhiza_maculata	2	1.27
Dicranella_staphylina	2	1.27
Elymus_repens	17	10.8
Epilobium_hirsutum	3	1.90
Epilobium_tetragonum	2	1.27
Equisetum_fluviatile	3	1.90
Equisetum_palustre	2	1.27
Euphrasia_nemorosa	2	1.27
Festuca_ovina	2	1.27
Fissidens_taxifolius	6	3.80
Galium_saxatile	2	1.27
Galium_verum	3	1.90
Geum_urbanum	2	1.27
Hordeum_secalinum	13	8.23
Juncus_acutiflorus_articulatus	6	3.80
Juncus_bufonius	3	1.90
Leontodon_autumnalis	2	1.27
Leontodon_taraxacoides	5	3.16
Lysimachia_nummularia	2	1.27
Malva_moschata	9	5.70
Molinia_caerulea	2	1.27
Myosotis_arvensis	4	2.53
Oenanthe_pimpinelloides	4	2.53
Ophioglossum_vulgatum	10	6.33
Poa_pratensis	17	10.8
Potentilla_anserina	3	1.90
Potentilla_hybrid	4	2.53
Ranunculus_sardous	2	1.27
Rumex_conglomeratus	6	3.80
Rumex_sanguineus	2	1.27
Senecio_aquaticus	2	1.27
Senecio_erucifolius	4	2.53
Sonchus_oleraceus	3	1.90
Stachys_palustris	2	1.27
Trifolium_medium	2	1.27
Trisetum_flavescens	2	1.27
Veronica_filiformis	5	3.16
Veronica_persica	2	1.27
Vicia_hirsuta	3	1.90
Vulpia_bromoides	2	1.27

Latent Community expression at survey sites.

Here is a summary of all the Latent Communities expressed at all the survey sites. Two features are immediately obvious:

1. Several LC may be expressed at a single site (Wood Field, Bushy Field, Lindfield Bridge).
2. Some sites have very low expression of any LC (Long Mead SE, SW; Pond field W). We can investigate these sites to find out what is going on.

The pages following show the expressions of individual communities by site. The scale on the left hand side is the percentage of the maximum possible expression.

Latent Community 1.

Latent Community 2.

Latent Community 3.

Latent Community 4.

Latent Community 5.

Latent Community 6.

Latent Community 7.

Latent Community 8.

3. Calculation of LC expression.

1. Write G_l for the graph of Latent Community l, of degree r_l (Latent communities are expressed as graphs in section 2 above. The degree of a graph is the number of links between the nodes; in this case the nodes are plant species.)
2. Write G_ls for the subgraph of G_l represented at site s.
3. Write A_ls for the subgraph of G_ls with associative links, and D_ls for the subgraph of G_ls with dissociative links.

Then the expression X_ls of Latent Community l at site s is X_ls = 100(a_ls-d_ls)/r_l

where a_ls is the degree (number of links) of A_ls and d_ls is the degree of D_ls.

The presence of associative dyads increases X_ls while dissociative dyads decrease X_ls. An LC with dissociative links can never be 100% represented; another option would be to normalise against the degree of A_l, the number of associative links in the parent LC. I decided against this because it is conceivable that there could be an LC with only dissociative links. Negative values of X_ls are possible.

4. Where next?

Can we glean any understanding of community organisation in our data by examining the species composition of the latent communities, and their site-specific expressions? There are hints of some possibilities:

• LC1 could be characterised as dyads with any of several rather interesting plants, but NOT Lolium perenne. The meadows where LC1 is most fully expressed are Gravetye East, Gravetye West and Plain Field North. I think I am correct that these are fields with a management history of intentional meadow restoration, and that would explain the presence of interesting plants; to the extent that L perenne is present at these sites (and I need to check up whether it is or not), it could be interpreted as a relic from former more intensive management.

• Latent Community 3 contains an assemblage of plants of damp or wet habitats. It is particularly expressed at Bushy Field, Daltons Meadow, Hanging Meadow, The Mead and White Coppice. This makes sense as these are all damp but well managed (from a wildflower meadow perspective).

• LC6 also includes plants from wet habitats, but maybe with a suggestion of higher nutrient level (Urtica dioica, Rumex crispus, Rumex acutifolius). Lindfield Bridge has the strongest expression of LC6; it is a riparine bank bordering a former agricultural field. It was pointed out in Section 2 that LC6 is anomalous in that the in_block probability is less than one of the out_block probabilities; in fact, less than the out_block probability with the other damp community, LC3, suggesting that these communities have a mutually exclusive relationship.

It will be interesting to use this tool to explore the data for further evidence of biotic or abiotic interactions which could further be tested (in principle at least) by field work or reference to literature.

5. Bibliography.

Munkemiller et al. 2020. Dos and Don’ts When Inferring Assembly Rules from Diversity Patterns. https://onlinelibrary.wiley.com/doi/full/10.1111/geb.13098.